# Potential GDP formula and output gap

## Potential GDP

Potential GDP is how much a country would produce if all of its resources were fully employed.

Typically, we assume that workers are the only resource in an economy which can be under-utilized*.

Therefore to calculate the potential GDP we wish to see how much actual GDP would be when we actually fully utilized all our workers - that is, there is no unemployment. However, instead of assuming that there is no unemployment, we look at the case where employment equals its natural rate of employment.

If you wish to see what determines the potential GDP (aka natural output) see this post.

## Potential GDP formula

The formula for calculating potential GDP is:

$\text{Potential GDP} = \frac{(\text{natural rate of employment})}{(\text{actual rate of employment})} * (\text{actual GDP})$

Typically we observe the unemployment rate not the employment rate. Therefore, given that the $\text{employment rate} = 1 - \text{unemployment}$ we can calculate potential GDP as:

$Potential GDP = \frac{(1 - \text{natural rate of unemployment})}{(1 - \text{actual rate of unemployment}) }* (\text{actual GDP})$

Now let's look at some examples.

## Example 1

Consider an economy where the natural rate of employment is 95% and the actual rate of employment is 90% and the GDP of the economy is 1.13 trillion dollars. We would calculate the potential GDP as follows:

(recall percentages can be converted to decimal by dividing them by 100.  e.g 95% = $\frac{95}{100} = 0.95$)

$\text{potential GDP} = \frac{0.95}{0.9}*1.13 = 1.19$

## Example 2

Consider an economy where the natural rate of unemployment is 3% and the actual rate of unemployment is 5% and the GDP of the economy is 1.42 trillion dollars. We would calculate the potential GDP as follows:

First, calculate the rates of employment:

$\text{natural rate of employment} = 1 - 0.03 = .97$

$\text{actual rate of employment} = 1 - 0.05 = .95$

$\text{potential GDP} = \frac{.97}{.95} *1.42 = 1.45$

## The output gap

The output gap (also known as GDP gap) is the difference between the potential GDP and actual GDP. The output gap formula is:

Output gap = Actual output - Potential output

In macroeconomics, output and GDP are used synonymously.

There is another formula that might be required which is the percentage GDP gap which is:

$\text{Percentage GDP gap} = \frac{(\text{Actual output}) - (\text{potential output})}{(\text{potential output})}$

## Examples

in Example 1 above the output gap is:

$\text{Output Gap}=1.13-1.19=-0.06\text{ trillion dollars}$

the Percentage GDP gap is

$\text{Percentage GDP gap}=\frac{(1.13 - 1.19)}{1.19} = 0.05$ (5%)

In Example 2 above the output gap is:

$\text{Output Gap}=1.42-1.45=-0.03\text{ trillion dollars}$

the Percentage GDP gap is

$\text{Percentage GDP gap} = \text{(1.42 - 1.45)}{1.45} = 0.02$ (2%)

When the output gap is negative the economy is said to be operating Below capacity or "underheating". Conversely, when the output gap is positive the economy is said to be operating above capacity or overheating.

* Economies also employ "capital" which are machines etc. which can also be under-utilized. However, for simplicity we tend to assume that they are always fully utilized.

##### 4 Responses
1. Percentage GDP gap is [(acutal output) - (potential output)] ÷ (potential output)

1. You are correct, my apologies.

2. its so much helpful, but how can i site the source please?

1. Unless you are using a specific calculation, I don't think any citation would be required in this case.